Getal & Ruimte (12e editie) - vwo wiskunde B
'Rekenen met logaritmen'.
| vwo wiskunde B | 5.4 Logaritmen |
opgave 1Bereken. 1p a \({}^{9}\!\log(81)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{9}\!\log(81) = {}^{9}\!\log(9^{2}) = 2\) 1p 1p b \({}^{9}\!\log(1)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{9}\!\log(1) = {}^{9}\!\log(9^{0}) = 0\) 1p 1p c \(\log(1\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(1\,000) = \log(10^{3}) = 3\) 1p 1p d \({}^{2}\!\log(\frac{1}{2})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{2}\!\log(\frac{1}{2}) = {}^{2}\!\log(2^{-1}) = -1\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{4}}\!\log(\frac{1}{64})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{4}}\!\log(\frac{1}{64}) = {}^{\frac{1}{4}}\!\log(\frac{1}{4}^{3}) = 3\) 1p 1p b \({}^{\frac{1}{2}}\!\log(4)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{2}}\!\log({}^{\frac{1}{2}}\!\log(4)) = {}^{\frac{1}{2}}\!\log(\frac{1}{2}^{-2}) = -2\) 1p 1p c \({}^{9}\!\log(9 \sqrt{9})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{9}\!\log(9 \sqrt{9}) = {}^{9}\!\log(9^{1} ⋅ 9^{\frac{1}{2}}) = {}^{9}\!\log(9^{1\frac{1}{2}}) = 1\frac{1}{2}\) 1p 1p d \({}^{4}\!\log(4^{4{,}4})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{4}\!\log(4^{4{,}4}) = 4{,}4\) 1p |